Reference books say that the name Addison means son of Adam, Addy being a pet form of Adam. (In the 12th century, Adam was one of the favourite boys' names in England.)
The earliest known use of the surname Addison in England was in 1308 - Adkin in 1191, Adcock in 1246, and Addy in 1327.In Scotland it was first noted in 1370.
The Addisons are of Bernician origin.The Bernician race was a mixture including Scots, Picts, Angles and Vikings.From 400 AD, or before, they lived on what is now the Scotland-England border.Their territory ranged from Edinburgh in the north, southwards to the north riding of Yorkshire in England.
The second king of Bernicia was Ada, so perhaps the Addisons were named after this king.